If you can't find the ringtone, or it didn't download: You may want to re-download the iTunes purchase:
Apple Support's online article: Use tones and ringtones with your iPhone or iPad - Apple Support
Eg: says:
"Go to Settings > Sounds & Haptics > Ringtones, then scroll to the top and tap Tone Store.
Your purchased tones and ringtones appear at the top of the list of sounds.
If .... your previous purchases aren't showing up, tap Download All Purchased Tones.
You might not see this option if you already downloaded all the tones that you purchased or if you haven't
purchased any tones. You might not be able to redownload some previously purchased tones.
Store availability and features might vary by country or region. Learn what's available in your country or region.
Any digital media you buy from Apple can be permanently downloaded on to an iPhone, iPad, Mac, or Windows PC. Learn more."
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Re: " ... they don’t let you download any ringtone from other sources"
Eg:
You can use Garageband app to shorten audio to the required length, and export as a ringtone to use on iPhone
Another discussion thread with the details: Can i use a saved or created mp3 ringtone? - Apple Community
